# Is stiffness of a beam the product of Young's modulus and second moment of area?

Is stiffness of a beam the product of Young's modulus and second moment of area? I read online that stiffness of a beam is function of the product of young's modulus and second moment of area. I cannot find any reference of the exact equation. Is it just the product of the young's modulus and the second moment of area or is there anything more? I don't know the deflection of the beam, I only know its young modulus and its second moment of area and I want to compare two beams based on that. How can I do it?

• Lookup "flexural rigidity" for beams. – ja72 Sep 13 '16 at 17:31

Take a clamped beam of length $\ell$. The deflection due to an end load is
$$\delta = \frac{F \ell^3}{3 E I}$$
The stiffness (in terms of force/displacement) is $$k =\frac{3 E I}{\ell^3}$$
where $E I$ is the young's modulus times the area moment. So the stiffness is proportional to what is called flexural rigidity. It represents the part of the stiffness that is dependent on the cross sectional shape and the material.